Dimensions and cotorsion pairs in recollements of extriangulated categories

Abstract

Let $(\mathcal{A},\mathcal{B},\mathcal{C})$ be a recollement of extriangulated categories. In this paper, we provide bounds on the coresolution dimensions of the subcategories involved in $\mathcal{A}$, $\mathcal{B}$ and $\mathcal{C}$. We show that a hereditary cotorsion pair in $\mathcal{B}$ can induce hereditary cotorsion pairs in $\mathcal{A}$ and $\mathcal{C}$ under certain conditions. Besides, we construct recollements of abelian categories from a recollement of extriangulated categories with respect to the hearts of cotorsion pairs.

19 pages